Robot Locomotion Group

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The goal of our research is to build machines which exploit their
natural dynamics to achieve extraordinary agility and efficiency.
In an age where "big data" is all the rage, we still have relatively limited data from robots in these regimes, and instead rely mostly on
existing models (e.g. from Lagrangian mechanics) and model-based optimization. We believe that deep connections are possible -- enabling very efficient optimization by exploiting structure in the governing equations -- and are working hard on both optimization algorithms and control applications.
Our current projects include dynamics and control for humanoid robots, robotic manipulation, and dynamic walking over rough terrain, flight control for aggressive maneuvers in unmanned aerial vehicles, feedback control for fluid dynamics and soft robotics, and connections between perception and control.

Locomotion Group Paper and Multimedia News

by Gregory Izatt and Geronimo Mirano and Edward Adelson and Russ Tedrake

We present an object-tracking framework that fuses
point cloud information from an RGB-D camera with tactile
information from a GelSight contact sensor. We propose that
GelSight can be treated as a source of dense local geometric
information, which we incorporate directly into a conventional
point-cloud-based articulated object tracker based on signed-
distance functions. Our implementation runs at 12 Hz using
an online depth reconstruction algorithm for GelSight and a
modified second-order update for the tracking algorithm. We
present data from hardware experiments demonstrating that the
addition of contact-based geometric information significantly improves the pose accuracy during contact, and provides robustness
to occlusions of small objects by the robots end effector.

In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force/torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit.

Maintaining balance is fundamental to legged robots. The most commonly used mechanisms for balance control are taking a step, regulating the center of pressure (ankle strategies), and to a lesser extent, changing centroidal angular momentum (e.g., hip strategies). In this paper, we disregard these three mechanisms, instead focusing on a fourth: varying center of mass height. We study a 2D variable-height center of mass model, and analyze how center of mass height variation can be used to achieve balance, in the sense of convergence to a fixed point of the dynamics. In this analysis, we pay special attention to the constraint of unilateral contact forces. We first derive a necessary condition that must be satisfied to be able to achieve balance. We then present two control laws, and derive their regions of attraction in closed form. We show that one of the control laws achieves balance from any state satisfying the necessary condition for balance. Finally, we briefly discuss the relative importance of CoM height variation and other balance mechanisms.

We present a method for robust high-speed quadrotor flight through unknown cluttered environments using a fast approximation of
collision probabilities. Motivated by experiments in which the difficulty of accurate state estimation was a primary limitati...

In order for robots to interact safely and intelligently
with their environment they must be able to reliably
estimate and localize external contacts. This paper introduces
CPF, the Contact Particle Filter, which is a general algorithm
for detecting and localizing external contacts on rigid body
robots without the need for external sensing. CPF finds external
contact points that best explain the observed external joint
torque, and returns sensible estimates even when the external
torque measurement is corrupted with noise. We demonstrate
the capability of the CPF to track multiple external contacts
on a simulated Atlas robot, and compare our work to existing
approaches.